Grounded in the Unified Theory of Acceptance and Use of Technology 2 (UTAUT2), this study investigates the interplay between key UTAUT2 constructs and motivation modeled by Self-Determination Theory (SDT) in shaping English as a Foreign Language (EFL) learners' behavioral intention and actual use of generative AI tools. Accordingly, three research questions were devised, including (1) What are the structural relationships between the UTAUT2 constructs for EFL learners to accept and use generative AI for English learning? (2) Does EFL learners' SDT motivation influence their behavioral intention toward and actual use of generative AI? and (3) What are the moderating effects of EFL learners' SDT motivation toward their acceptance and use of generative AI? A comprehensive survey involving 620 Chinese undergraduates assessed their technology acceptance and SDT motivation of generative AI tools in the EFL learning context. Confirmatory factor analysis and structural equation modeling were employed to analyze the data. Results indicate robust model fit indices, both with and without considering moderating effects. Performance expectancy, effort expectancy, social influence, hedonic motivation, habit, and SDT motivation serve as significant predictors of EFL learners' behavioral intention towards generative AI tools, while price value does not demonstrate a significant impact on behavioral intention. Additionally, behavioral intention and SDT motivation jointly and significantly predict EFL learners' actual use of the technology. Importantly, introducing SDT motivation as a moderator unveils additional insights. Facilitating conditions exerts a significant influence on both behavioral intention and actual use, indicating a significant moderating effect of SDT moderation on these two pathways. Moreover, SDT motivation also significantly moderates the relationships between facilitating conditions and behavioral intention as well as between facilitating conditions and actual use, adding depth to our understanding of the nuanced interplay between motivation and technology acceptance of generative AI tools. The study concludes with insightful discussions on the findings, acknowledging the robust contributions and highlighting areas for future research to further enrich our understanding of EFL learners' adoption of generative AI tools in the context of UTAUT2 with SDT moderation.